COVID-19 Progression

Introduction

library(tidyverse)
library(magrittr)
library(lubridate)
library(scales)
library(matrixStats)
library(ggrepel)
library(broom)
library(glue)
library(pander)
library(plotly)
panderOptions("big.mark", ",")
panderOptions("table.split.table", Inf)
panderOptions("table.style", "rmarkdown")
theme_set(theme_bw())

Disclaimer: This very simple report was prepared by a bioinformatician with no experience in epidemiology or virology, and as such should be treated simply as an alternate viewpoint on the data, which I was simply unable to find elsewhere. Many other people exist with much greater expertise on this subject. However, I do hope this provides a useful perspective which is able to add constructively to the wider discussion.

Data was sourced from Johns Hopkins University (https://coronavirus.jhu.edu/), using the datasets provided by JHU at https://github.com/CSSEGISandData/COVID-19. JHU data is updated every 24 hours at approximately 23:59(UTC), which is about 10:30AM in Adelaide. As a result Australian numbers may lag local media reports.

Additionally, the official government figures at www.health.gov.au appear to lag media reports, likely to ensure accuracy of the official numbers. The official Australian numbers are not used for this analysis, instead relying on those provided by JHU. However, JHU are extremely careful and comprehensive in their sourcing of numbers and significant disparity is not expected. Live updates for Australia are available from https://covid-19-au.github.io/ for those who would like an up to the minute breakdown of confirmed cases.

confirmed <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Confirmed.csv") %>%
    read_csv() %>%
    pivot_longer(
        cols = ends_with("20"),
        names_to = "date",
        values_to = "confirmed"
    )  %>%
    mutate(
        date = str_replace_all(
            date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
        ) %>%
            ymd()
    ) %>%
    dplyr::rename(
        Country = `Country/Region`
    ) %>%
    dplyr::mutate(
        Country = case_when(
            `Province/State` == "Hubei" ~ "China (Hubei)",
            `Province/State` == "Hong Kong" ~ "Hong Kong",
            grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
            !grepl("China", Country) ~ Country
        )
    ) %>%
    dplyr::filter(
        !is.na(confirmed)
    ) # %>%
  # bind_rows(
  #   tibble(
  #     Country = "Australia",
  #     date = ymd("2020-03-20"),
  #     confirmed = 876
  #   )
  # )

Population sizes for the most impacted countries were manually obtained from https://www.worldometers.info/ and should not be considered as authoritative. Given the disparity of infection within China, China was broken into Hubei Province, Hong Kong and the rest of China. As an open acknowledgement of the crudeness of population values, population estimates for Hubei Province were taken from the 2018 estimates given by Statista.com. This particular population estimate is likely to be low, and as a result confirmed case rates for Hubei province may be an overestimate, and consequently, confirmed case rates for the rest of China may also be an underestimate.

Confirmed cases of COVID-19 as provided by the Chinese Government have been discussed elsewhere as unusual, and data appears potentially unreliable. In this analysis, discussions regarding accurate Chinese reporting are not considered further and data is simply presented as supplied by JHU.

However, all countries are likely to contain many unreported cases given the incomplete testing regimes in place for most countries. Similarly, reporting in many countries may have features that cause concerns regarding data integrity and this makes comparison across countries difficult.

hb <- 59170000
pops <- tribble(
    ~Country, ~Population,
    "Australia", 25499884,
    "Austria", 9006398,
    "Belgium", 11575214,
    "Brazil", 212129490,
    "Canada", 37742154,
    "China (Hubei)", hb,
    "China (Other)", 1408526449 - hb,
    "Czechia", 10703010,
    "Denmark", 5786274,
    "Finland", 5538181,
    "France", 65273511,
    "Germany", 83783942,
    "Greece", 10423054,
    "Hong Kong", 7479307,
    "Italy", 60486925,
    "Iran", 83677594,
    "Ireland", 4921810,
    "Israel", 8615601,
    "Japan", 126476461,
    "Korea, South", 51269185,
    "Malaysia", 32245488,
    "Netherlands", 17134872,
    "New Zealand", 4811065,
    "Norway", 5408930,
    "Pakistan",  219629013,
    "Portugal", 10196709,
    "Qatar", 2866531,
    "Singapore", 5836728,
    "Spain", 46754778,
    "Sweden", 10081035,
    "Switzerland", 8654622,
    "Taiwan*", 23804524,
    "United Arab Emirates", 9856053, 
    "United Kingdom", 67886011,
    "US", 331002651
)

Results & Discussion

Cumulative Incidence Rates

All information presented in the section below is effectively the cumulative, confirmed incidence rate. Recovered patients and those who have passed away are still included in these numbers. Testing rates and results are also not included, and these may be highly informative if able to be sourced accurately.

confirmed %>%
    group_by(Country, date) %>%
    summarise(confirmed = sum(confirmed)) %>%
    ungroup() %>%
    group_by(Country) %>%
    dplyr::filter(
        date == max(date)
    ) %>%
    ungroup() %>%
    right_join(pops) %>%
    mutate(
        rate = 1e6*confirmed / Population
    ) %>%
    arrange(desc(rate)) %>%
    dplyr::slice(1:25) %>%
    mutate(
        rate = sprintf("%.1f", rate),
        Population = comma(Population)
    ) %>%
    rename_at(vars(everything()), str_to_title) %>%
    rename(`Rate (Cases per Million)` = Rate) %>%
    pander(
        justify = "lrrrr",
        caption = paste(
            "The", nrow(.), "most impacted populations studied here and shown as a proportion of total population.", 
            "The final column provides the latest confirmed infection rate as cases per million people.",
            "Whilst the virus spreads with no regard to population size, the rate as shown here indicates the degree of stress which each country's health-care system is likely to be experiencing.",
            "Several countries shown here have not attracted much media attention due lower case numbers than China and Italy, but are likely to be experiencing significant duress."
        )
    )

The 25 most impacted populations studied here and shown as a proportion of total population. The final column provides the latest confirmed infection rate as cases per million people. Whilst the virus spreads with no regard to population size, the rate as shown here indicates the degree of stress which each country’s health-care system is likely to be experiencing. Several countries shown here have not attracted much media attention due lower case numbers than China and Italy, but are likely to be experiencing significant duress.

Country	Date	Confirmed	Population	Rate (Cases per Million)
China (Hubei)	2020-03-19	67,800	59,170,000	1145.9
Italy	2020-03-19	41,035	60,486,925	678.4
Switzerland	2020-03-19	4,075	8,654,622	470.8
Spain	2020-03-19	17,963	46,754,778	384.2
Norway	2020-03-19	1,746	5,408,930	322.8
Austria	2020-03-19	2,013	9,006,398	223.5
Iran	2020-03-19	18,407	83,677,594	220.0
Denmark	2020-03-19	1,225	5,786,274	211.7
Germany	2020-03-19	15,320	83,783,942	182.9
France	2020-03-19	10,947	65,273,511	167.7
Korea, South	2020-03-19	8,565	51,269,185	167.1
Qatar	2020-03-19	460	2,866,531	160.5
Belgium	2020-03-19	1,795	11,575,214	155.1
Netherlands	2020-03-19	2,467	17,134,872	144.0
Sweden	2020-03-19	1,439	10,081,035	142.7
Ireland	2020-03-19	557	4,921,810	113.2
Israel	2020-03-19	677	8,615,601	78.6
Portugal	2020-03-19	785	10,196,709	77.0
Finland	2020-03-19	400	5,538,181	72.2
Czechia	2020-03-19	694	10,703,010	64.8
Singapore	2020-03-19	345	5,836,728	59.1
US	2020-03-19	13,677	331,002,651	41.3
Greece	2020-03-19	418	10,423,054	40.1
United Kingdom	2020-03-19	2,716	67,886,011	40.0
Malaysia	2020-03-19	900	32,245,488	27.9

minToInclude <- 5
startingPoint <- 1
nDays <- confirmed %>%
  dplyr::filter(Country == "Hong Kong") %>% 
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  left_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>% 
  dplyr::filter(rate > startingPoint) %>% 
  nrow() %>%
  subtract(1)

p <- confirmed %>%
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  right_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>%
  group_by(Country) %>%
  dplyr::filter(
    max(rate) > minToInclude
  ) %>%
  ungroup() %>%
  split(f = .$Country) %>%
  lapply(function(x, r = startingPoint){
    std <- min(dplyr::filter(x, rate > r)$date)
    x %>%
      dplyr::filter(date >= std) %>%
      mutate(days = date - std)
  }) %>%
  bind_rows() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  arrange(date) %>%
  mutate(Country = fct_inorder(Country)) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(Days, Rate, colour = Country, Date = Date, Confirmed = Confirmed)
  ) +
  geom_segment(
    aes(x, y, xend = xmax, yend = ymax),
    data = tibble(
      x = 0,
      y = 1,
      xmax = c(20.5, 41, nDays),
      ymax = 2^(xmax/ c(2, 4, 8))
    ),
    inherit.aes = FALSE,
    colour = "grey70",
    linetype = 2
  ) + 
  geom_text(
        aes(xmax, ymax, label = label),
    data = tibble(
      xmax = c(20.5, 41, nDays),
      rate = c(2, 4, 8),
      ymax = 2^(xmax/ rate),
      label = glue::glue("Doubling in\n {rate} days")
    ),
    colour = "grey70",
    inherit.aes = FALSE
  ) +
  geom_point() +
  geom_line() +
  scale_x_continuous(
    expand = expand_scale(mult = c(0, 0.05)),
  ) +
  scale_y_log10(
    expand = expand_scale(mult = c(0, 0.05)),
  ) +
  xlab(
    paste(
      "Days since passing", 
      startingPoint,
      "confirmed case/million"
    )
  ) +
  ylab("Confirmed Infection Rate (cases/million)")

ggplotly(
  p, 
  tooltip = c(
    "Days", "Rate", "Country", "Date", "Confirmed"
  )) 

Confirmed cases of COVID-19 for countries where the infection rate has exceeded 5 cases/million. Data is only shown for the first 53 calendar days since passing 1 confirmed case/million. Note that from the day records begin in this dataset, the confirmed infection rate in Hubei was 7.59 confirmed cases/million. Diagonal grey lines indicate a doubling in the infection rate every 2, 4, or 8 days. To hide a country, click on the country in the plot legend. Clicking again on the country in the legend will restore the data within the plot. Countries are shown in order of the date at which they passed the 1 confirmed case/million mark. Due to the number of countries shown, you may need to scroll through the legend. Regions of the plot are also able to be zoomed interactively. Please note the y-axis is shown on the logarithmic scale, so that a series of points which appear to be diagonal will indicate exponential growth. The flatter the line, the slower the growth and a perfectly horizontal line would indicate zero growth, or no new confirmed cases.

All figures and tables presented here simply aim to show an alternative viewpoint on the data. Every way to view COVID-19 data will mask important features, and the values shown here do not take into account vital factors such as population density, variability of infection across regions within countries, social culture and demographics. Many countries may not be directly comparable for a combination of the above factors. It is simply to view the data through the lens of a country’s population size using a value which should be easily interpretable.

In the above plot:

• Only countries are shown where the infection rate has surpassed 5 cases/million. This was a completely arbitrary choice, but seemed likely to indicate a level of COVID-19 infection which posed noticeable community risk
• The choice of “Days since passing 1 case/million” was also arbitrary, but seemed to be a useful way of enabling the comparison of COVID-19 progression across countries

Additionally, Australia’s spread of the virus appears marginally slower than many other countries.

• This may be a reflection of Australian geography or our tendency to have large personal space requirements
• This may also be a reflection of the pre-emptive strategies already being taken by the population and government
• Overall, the Australian infection rate brings mild relief that we are doing a little better than many other countries. However testing rates are far lower than in countries like South Korea and many genuine cases are likely to be undetected
• Despite the above, Australia is still clearly in the exponential growth phase with no sign of the growth levelling out. Infections are currently doubling in slightly less than 4 days, meaning Australian infections are expected to exceed 1,362 by Monday 23 March, 2020.
• Using an estimated population size of 25,499,884, the total percentage of the Australian population confirmed as infected currently sits at 0.003%.

Turning to other countries beyond Australia:

• Only South Korea,and China appear to have brought the virus under some level of control. The infection rate currently sits around 167.1 per million for South Korea and 1145.9 per million for Hubei Province. This can also be thought of as 0.0167% and 0.1146% of the total populations respectively. Note that despite these apparently low percentages, the actual numbers of deaths and hospitalisations are extremely non-trivial and the real impacts of these numbers cannot be treated lightly.
• Japan’s early measures also appear to be highly effective, however the recent growth in infections within Singapore should serve as a caution
• Some of the above countries (e.g. Norway, Denmark) appear to be in the early stages of levelling out, indicating that the initial exponential growth phase may be ending in these countries.
• Other countries such as Italy and the UK are clearly still in an exponential growth phase.
• US numbers may also be unreliable given the low rates of testing and numerous anecdotal stories of suspected infections

Currently Active Infections

As an alternative viewpoint, the numbers of recovered and deceased patients have been removed from the above plot to provide an estimate of the currently active infections.

recovered <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Recovered.csv") %>%
    read_csv() %>%
    pivot_longer(
        cols = ends_with("20"),
        names_to = "date",
        values_to = "recovered"
    )  %>%
    mutate(
        date = str_replace_all(
            date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
        ) %>%
            ymd()
    ) %>%
    dplyr::rename(
        Country = `Country/Region`
    ) %>%
    dplyr::mutate(
        Country = case_when(
            `Province/State` == "Hubei" ~ "China (Hubei)",
            `Province/State` == "Hong Kong" ~ "Hong Kong",
            grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
            !grepl("China", Country) ~ Country
        )
    )
deaths <- url("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Deaths.csv") %>%
    read_csv() %>%
    pivot_longer(
        cols = ends_with("20"),
        names_to = "date",
        values_to = "deaths"
    )  %>%
    mutate(
        date = str_replace_all(
            date, "(.+)/(.+)/(.+)", "20\\3-\\1-\\2"
        ) %>%
            ymd()
    ) %>%
    dplyr::rename(
        Country = `Country/Region`
    ) %>%
    dplyr::mutate(
        Country = case_when(
            `Province/State` == "Hubei" ~ "China (Hubei)",
            `Province/State` == "Hong Kong" ~ "Hong Kong",
            grepl("China", Country) & !`Province/State` %in% c("Hubei", "Hong Kong") ~ "China (Other)",
            !grepl("China", Country) ~ Country
        )
    )

p2 <- confirmed %>%
  dplyr::filter(
    !str_detect(Country, "Other")
  ) %>%
  left_join(recovered) %>%
  left_join(deaths) %>%
  mutate(
    active = confirmed - recovered - deaths
  ) %>%
  group_by(
    Country, date
  ) %>%
  summarise(
    active = sum(active),
    confirmed = sum(confirmed),
    recovered = sum(recovered),
    deaths = sum(deaths)
  ) %>%
  right_join(pops) %>%
  mutate(rate = 1e6*active / Population)  %>%
  dplyr::filter(
    max(rate) > minToInclude
  ) %>%
  ungroup() %>%
  split(f = .$Country) %>%
  lapply(function(x, r = startingPoint){
    std <- min(dplyr::filter(x, rate > r)$date)
    x %>%
      dplyr::filter(date >= std) %>%
      mutate(days = date - std)
  }) %>%
  bind_rows() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  arrange(date) %>%
  mutate(Country = fct_inorder(Country)) %>%
  rename_all(str_to_title) %>%
  ggplot(
    aes(
      x = Days, y = Rate, colour = Country, 
      Date = Date, Active = Active,
      Confirmed = Confirmed, Recovered = Recovered,
      Deaths = Deaths
      )
  ) +
  geom_segment(
    aes(x, y, xend = xmax, yend = ymax),
    data = tibble(
      x = 0,
      y = 1,
      xmax = c(20.5, 41, nDays),
      ymax = 2^(xmax/ c(2, 4, 8))
    ),
    inherit.aes = FALSE,
    colour = "grey70",
    linetype = 2
  ) + 
  geom_text(
        aes(xmax, ymax, label = label),
    data = tibble(
      xmax = c(20.5, 41, nDays),
      rate = c(2, 4, 8),
      ymax = 2^(xmax/ rate),
      label = glue::glue("Double in\n {rate} days")
    ),
    colour = "grey70",
    inherit.aes = FALSE
  ) +
  geom_point() +
  geom_line() +
  scale_y_log10() +
  xlab(
    paste(
      "Days since passing", 
      startingPoint, 
      "confirmed active case/million"
    )
  ) +
  ylab("Confirmed Active Infections (cases/million)")

ggplotly(p2) 

Confirmed active cases of COVID-19 for countries where the confirmed infection rate has exceeded 5 cases/million. Data is only shown for the first 53 calendar days since passing 1 confirmed case/million. Due to difficulties introduced by the currently reported low active infection rate outside Hubei province, data from China has been excluded from this plot, with the exception of Hubei. To hide a country, click on the country in the plot legend. Clicking again on the country in the legend will restore the data within the plot. Countries are shown in order of the date at which they passed the 1 confirmed active case/million mark. Due to the number of countries shown, you may need to scroll through the legend. Regions of the plot are also able to be zoomed interactively. Please note the y-axis is shown on the logarithmic scale, so that a series of points which appear to be diagonal will indicate exponential growth/decay.

Notable features of this perspective are:

• No deaths from confirmed cases have been reported in Singapore. Despite recent increases in active infections, has “flattening the curve” been successful?
• Active infection rates in South Korea are currently declining
• According to these figures, active infections within Hubei province are also significantly declining

Fatality, Recovery and Active Infection Rates

Summarising all available data from all countries:

• The current fatality rate is 4.1%. This may be a function of under-reporting of true cases and may be an overestimate
• The current recovery rate is 35.0%. Given the level of under-reporting this may also be highly inaccurate.
• At this point, 61.0% of all confirmed infections are considered as ‘active’.

p4 <- confirmed %>%
  dplyr::filter(
    confirmed > 100,
    Country != "Cruise Ship"
  ) %>%
  left_join(recovered) %>%
  left_join(deaths) %>%
  mutate(
    active = confirmed - recovered - deaths
  ) %>%
  group_by(
    Country, date
  ) %>%
  summarise(
    confirmed = sum(confirmed),
    active = sum(active),
    recovered = sum(recovered),
    deaths = sum(deaths)
  ) %>%
  group_by(Country) %>%
  dplyr::filter(date == max(date)) %>%
  ungroup() %>%
  mutate(
    active = 100*active / confirmed,
    recovered = 100*recovered / confirmed,
    fatalities = 100*deaths / confirmed
  ) %>%
  dplyr::filter(active < 100) %>%
  arrange(desc(confirmed)) %>%
  mutate(Country = fct_inorder(Country)) %>%
  pivot_longer(
    cols = c(active, recovered, fatalities),
    names_to = "Status",
    values_to = "Percentage"
  ) %>%
  mutate(
    Status = str_to_title(Status),
    Status = factor(
      Status, 
      levels = c("Active", "Recovered", "Fatalities")
    ),
    Percentage = round(Percentage, 2)
  ) %>%
  mutate(confirmed = comma(confirmed)) %>%
  rename(Confirmed = confirmed) %>%
  ggplot(
    aes(
      Country, Percentage,
      fill = Status, cases = Confirmed
    )
  ) +
  geom_col() +
  scale_fill_manual(
    values = c(
      Active = "blue",
      Recovered = "green",
      Fatalities = "red"
      )
  ) +
  scale_y_continuous(expand = expand_scale(0, 0)) +
  coord_flip() +
  theme(
    legend.position = "none"
  )

ggplotly(p4)

Fatality, Recovery and Active Infection rates for countries which have exceeded 100 confirmed cases. Countries are shown in order of the number of confirmed cases.

Comparison of Countries

In order to summarise which countries are the most similar to each other, a Principal Component Analysis was performed. This enables the multi-dimensional data of the above plots to summarised in two dimensions. As missing data cannot be included in this analysis, several countries which are at earlier comparative time-points than Australia were omitted from this analysis.

nDays <- confirmed %>% 
  dplyr::filter(Country == "Australia") %>% 
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  left_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>% 
  dplyr::filter(rate > startingPoint) %>% 
  nrow() %>%
  subtract(1)

pca <- confirmed %>%
  group_by(Country, date) %>%
  summarise(confirmed = sum(confirmed)) %>%
  ungroup() %>%
  right_join(pops) %>%
  mutate(
    rate = 1e6*confirmed / Population
  ) %>%
  group_by(Country) %>%
  dplyr::filter(
    max(rate) > minToInclude
  ) %>%
  ungroup() %>%
  split(f = .$Country) %>%
  lapply(function(x, r = startingPoint){
    std <- min(dplyr::filter(x, rate > r)$date)
    x %>%
      dplyr::filter(date >= std) %>%
      mutate(days = date - std)
  }) %>%
  bind_rows() %>%
  mutate(
    days = as.integer(days),
    rate = round(rate, 2)
  ) %>%
  dplyr::filter(days <= nDays) %>%
  dplyr::select(-date, -confirmed, -Population) %>%
  pivot_wider(
    values_from = rate,
    names_from = days
  ) %>%
  as.data.frame() %>%
  column_to_rownames("Country") %>%
  as.matrix() %>%
  .[!rowAnyNAs(.),] %>%
  log() %>%
  prcomp() 

pca$x %>%
  as.data.frame() %>%
  rownames_to_column("Country") %>%
  ggplot(aes(PC1, PC2, label = Country)) +
  geom_point() +
  geom_text_repel() +
  xlab(
    paste0(
      "PC1 (", 
      percent(summary(pca)$importance["Proportion of Variance","PC1"], accuracy = 0.1), 
      ")"
      )
  ) +
    ylab(
    paste0(
      "PC2 (", 
      percent(summary(pca)$importance["Proportion of Variance","PC2"], accuracy = 0.1), 
      ")"
      )
  )

Dimensional reduction showing which countries are most similar to each other at the 18 day mark. The value 18 days was chosen as this marks how long Australia has been passed 1 case/million. Countries which have not progressed beyond 1 case/million for 18 days or more are not shown. Principal Component 1, on the x-axis, corresponds to the greatest source of variability within the data (92.5%), and countries which appear near each other along this axis can be assumed to be showing similar growth in confirmed infection rates at this time point. Separation along the y-axis is less significant, but also worthy of note, as this represents 5.0% of variability within the data. At this early point, Australia’s cumulative, confirmed infection rate is diverging from countries which have responded well and is more similar to Israel. This is strongly suggestive the early measures instituted in Australia have been inadequate.

States Within Australia

Comparison of Confirmed Infection Rates

Australian State populations were taken from the ABS Website and were accurate in Sept 2019. The difference with previous estimates used above was within 0.04%, and as such no adjustments were made.

ausPops <- tribble(
  ~State, ~Population,
  "New South Wales",    8117976,
  "Victoria", 6629870,
   "Queensland", 5115451,
  "South Australia", 1756494,
  "Western Australia", 2630557,
  "Tasmania", 535500,
  "Northern Territory", 245562,
  "Australian Capital Territory", 428060
)

minRate <- 3
p5 <- confirmed %>%
  dplyr::filter(
    Country == "Australia"
  ) %>%
  dplyr::rename(State = `Province/State`) %>%
  left_join(ausPops) %>%
  mutate(
    Rate = round(1e6*confirmed / Population, 2),
    Date = format.Date(date, "%d-%B")
  ) %>%
  dplyr::filter(
    !is.na(Population),
    !str_detect(State, "Territory"),
    Rate > minRate
  ) %>%
  arrange(date) %>%
  mutate(
    State = fct_inorder(State)
  ) %>%
  dplyr::rename(
    Confirmed = confirmed
  ) %>%
  ggplot(
    aes(
      x = date, y = Rate, colour = State, 
      label = Date, key = Confirmed
      )
  ) +
  geom_point() +
  geom_smooth(
    method = "lm", 
    se = FALSE,
    show.legend = FALSE
  ) +
  geom_line(linetype = 3) +
  scale_y_log10() +
  labs(
    x = "Date",
    y = "Confirmed Infection Rate (cases/million)"
  )
# Hide the tooltip from the regression lines
n <- length(levels(p5$data$State))
p5 <- ggplotly(p5, tooltip = c("Date", "Rate", "State", "Confirmed"))
regIndex <- seq(n + 1, length.out = n, by = 1)
p5$x$data[regIndex] <- lapply(
  p5$x$data[regIndex],
  function(x){
  x$hoverinfo <- "none"
  x
})

p5

Infection rates for each state with data beginning for each state once 3 confirmed cases /million was exceeded. Linear regression lines are shown for each state as the solid lines, with NSW perhaps showing a slightly increased rate of infection within the population. Once again, the y-axis is on a logarithmic scale indicating exponential growth is occurring. States are shown in order of the initial date they passed 3 cases/million. Due to the low population sizes in the ACT and NT, these territories were omitted.

Statistical Analysis

In order to test whether the infection rates are different between states, a linear regression model was fit. \(\log_{10}\)(Cumulative Confirmed Infection Rate) was assigned as the response variable with predictor variables being the State and Date. Each State was assigned it’s own intercept and slope by use of an interaction term (i.e. State:date). Given the potentially larger slope in NSW, this state was set as the baseline, with each other slope (i.e. interaction term) being presented as the difference in slope between each state and NSW. In this way comparisons against NSW were performed, but no comparisons between other states were performed.

Differences in the State-level intercepts are not particularly relevant, apart from capturing the initial cumulative confirmed infection rate exceeded 3 cases / million. Differences between State-level slopes and NSW however, are of great interest, and as such only the slopes are shown. For NSW (Term = date) this captures the actual slope of the daily change in infection rate, whilst for all other States, this represents the difference between the daily change in infection rate for that State in comparison to NSW. Only differences in slope with an FDR-adjusted p-value < 0.05 are of particular interest. For those States which appear to be of interest, a negative value indicates an infection rate increasing more slowly than NSW, whilst a positive value indicates the opposite..

lm <- confirmed %>%
  dplyr::filter(
    Country == "Australia"
  ) %>%
  dplyr::rename(State = `Province/State`) %>%
  left_join(ausPops) %>%
  mutate(
    Rate = round(1e6*confirmed / Population, 2),
    Date = format.Date(date, "%d-%B")
  ) %>%
  dplyr::filter(
    !is.na(Population),
    !str_detect(State, "Territory"),
    Rate > minRate
  ) %>%
  arrange(desc(confirmed)) %>%
  mutate(
    State = fct_inorder(State)
  ) %>%
  dplyr::rename(
    Confirmed = confirmed
  ) %>%
  with(
    lm(log10(Rate) ~ (State + date)^2)
  ) 

lm %>%
  tidy() %>%
  mutate(
    FDR = p.adjust(p.value, method = "fdr"),
    term = str_remove_all(term, "State")
  ) %>%
  rename(
    Term = term,
    Estimate = estimate,
    SE = std.error,
    `T` = statistic,
    p = p.value
  ) %>%
  dplyr::filter(
    str_detect(Term, "date")
  ) %>%
  mutate(
    Estimate = sprintf("%.4f", Estimate),
    SE = sprintf("%.3f", SE),
    `T` = sprintf("%.2f", `T`),
    p = case_when(
      p < 1e-4 ~ sprintf("%.2e", p),
      p >= 1e-4 ~ sprintf("%.4f", p)
    ),
    FDR = case_when(
      FDR < 1e-4 ~ sprintf("%.2e", FDR),
      FDR >= 1e-4 ~ sprintf("%.4f", FDR)
    )
  ) %>%
  pander(
    justify = "lrrrrr",
    emphasize.strong.rows = which(
      as.numeric(.$FDR) < 0.05 & .$Term != "date"
      ),
    caption = paste(
      "*Results of linear regression analysis", 
      "comparing the slopes of lines which track __daily",
      "change in cumulative confirmed infection rates__,",
      "scaled for population size in each state.",
      "Intercept terms are not shown.",
      "All states are shown in comparison to NSW", 
      "with Queensland and Victoria appearing to show", 
      "infection rates increasing __faster__ than in NSW,",
      "whilst SA appears to be progressing at a __slower",
      "rate than NSW__.",
      "No difference was evident between WA and NSW or TAS and NSW.", 
      "These results are less conclusive than they may",
      "initially appear as the multiple days at the", 
      "same count for SA and TAS may have lead to",
      "violations of model assumptions.", 
      "Whilst diagnostic plots visually appeared",  
      "to be within acceptable bounds for real data,",
      "the fitted model failed the Shapiro-Wilk Test",
      "for normality", 
      paste0(
        "(p = ", 
        sprintf(
          "%.4f", shapiro.test(resid(lm))$p.value
        ),
        ")."
      ),
      "Assuming these results hold, it can be inferred",
      "that the increase in infection rate for SA", 
      "is also lower than in QLD and VIC.*"
    )
  )

Results of linear regression analysis comparing the slopes of lines which track daily change in cumulative confirmed infection rates, scaled for population size in each state. Intercept terms are not shown. All states are shown in comparison to NSW with Queensland and Victoria appearing to show infection rates increasing faster than in NSW, whilst SA appears to be progressing at a slower rate than NSW. No difference was evident between WA and NSW or TAS and NSW. These results are less conclusive than they may initially appear as the multiple days at the same count for SA and TAS may have lead to violations of model assumptions. Whilst diagnostic plots visually appeared to be within acceptable bounds for real data, the fitted model failed the Shapiro-Wilk Test for normality (p = 0.0081). Assuming these results hold, it can be inferred that the increase in infection rate for SA is also lower than in QLD and VIC.

Term	Estimate	SE	T	p	FDR
date	0.0836	0.004	21.19	2.03e-28	1.26e-27
Queensland:date	0.0180	0.008	2.36	0.0219	0.0329
Victoria:date	0.0216	0.009	2.50	0.0152	0.0304
Western Australia:date	0.0118	0.009	1.36	0.1777	0.1777
South Australia:date	-0.0146	0.006	-2.61	0.0116	0.0304
Tasmania:date	-0.0118	0.006	-1.86	0.0685	0.0825

coef(lm) %>% 
  enframe(name = "Term", value = "coef") %>%
  dplyr::filter(str_detect(Term, "date")) %>%
  mutate(
    slope = case_when(
      str_detect(Term, "State") ~ coef[[1]] + coef,
      !str_detect(Term, "State") ~ coef
    ),
    Term = str_remove(Term, "State"),
    State = str_remove(Term, ":date"),
    State = str_replace(State, "date", "New South Wales")
    ) %>%
  left_join(
    confirmed %>% 
      dplyr::filter(
        Country == "Australia", 
        date == max(date)
      ) %>% 
      rename(State = `Province/State`) %>%
      dplyr::select(State, date, confirmed)
  ) %>%
  mutate(
    predicted = round(10^slope*confirmed, 0),
    slope = percent(10^slope, accuracy = 0.1),
  ) %>%
  dplyr::select(
    State, 
    `Expected Daily Increase` = slope,
    `Most Recent` = confirmed,
    `Predicted For Next Day` = predicted
    ) %>%
  pander(
    justify = "lrrr",
    caption = paste(
      "Results from linear regression shown as the",
      "expected daily increase in cases for the",
      "current exponential growth phase.",
      "Most recent values were taken from the official",
      "figures on",
      confirmed %>%
        dplyr::filter(Country == "Australia") %>%
        .[["date"]] %>%
        max() %>%
        format("%d %B, %Y."),
      "Predictions are for",
      confirmed %>%
        dplyr::filter(Country == "Australia") %>%
        .[["date"]] %>%
        max() %>%
        add(1) %>%
        format("%d %B, %Y."),
      "Standard errors for predictions have not been included."
    )
  )

Results from linear regression shown as the expected daily increase in cases for the current exponential growth phase. Most recent values were taken from the official figures on 19 March, 2020. Predictions are for 20 March, 2020. Standard errors for predictions have not been included.

State	Expected Daily Increase	Most Recent	Predicted For Next Day
New South Wales	121.2%	307	372
Queensland	126.4%	144	182
Victoria	127.4%	121	154
Western Australia	124.6%	52	65
South Australia	117.2%	42	49
Tasmania	118.0%	10	12

Testing

Taking the testing numbers manually from https://covid-19-au.github.io/, the number of tested individuals in each state was assessed as a function of State population size. All results are valid at the time of report generation.

tribble(
  ~State, ~Tested,
  "New South Wales", 40651,
  "Queensland", 29579,
  "Victoria", 19337,
  "Western Australia", 8603,
  "South Australia", 13000,
  "Tasmania", 807,
  "Australian Capital Territory", 2062
) %>%
  left_join(
    confirmed %>%
      dplyr::filter(
        date == max(date)
      ) %>%
      rename(
        State = `Province/State`
      )
  ) %>%
  left_join(ausPops) %>%
  mutate(
    `Population Proportion` = Tested / Population,
    `Proportion Positive` = confirmed / Tested,
    `Proportion Negative` = 1 - `Proportion Positive`
  ) %>%
  dplyr::select(
    State, Tested, contains("Prop")
  ) %>%
  arrange(desc(`Population Proportion`)) %>%
  mutate_at(
    vars(contains("Prop")),
    percent,
    accuracy = 0.01
  ) %>%
  pander(
    justify = "lrrrr",
    caption = paste(
      "*COVID-19 testing scaled by State population size.",
      "Confirmed cases are assumed to be the tests",
      "returning a positive result.",
      "The current numbers available for SA are a", 
      "lower limit, so in reality, the proportion of",
      "the population tested is higher, as is the",
      "proportion of tests returning a negative result.*"
    )
  )

COVID-19 testing scaled by State population size. Confirmed cases are assumed to be the tests returning a positive result. The current numbers available for SA are a lower limit, so in reality, the proportion of the population tested is higher, as is the proportion of tests returning a negative result.

State	Tested	Population Proportion	Proportion Positive	Proportion Negative
South Australia	13,000	0.74%	0.32%	99.68%
Queensland	29,579	0.58%	0.49%	99.51%
New South Wales	40,651	0.50%	0.76%	99.24%
Australian Capital Territory	2,062	0.48%	0.19%	99.81%
Western Australia	8,603	0.33%	0.60%	99.40%
Victoria	19,337	0.29%	0.63%	99.37%
Tasmania	807	0.15%	1.24%	98.76%

R Session Information

R version 3.6.3 (2020-02-29)

Platform: x86_64-pc-linux-gnu (64-bit)

locale: LC_CTYPE=en_AU.UTF-8, LC_NUMERIC=C, LC_TIME=en_AU.UTF-8, LC_COLLATE=en_AU.UTF-8, LC_MONETARY=en_AU.UTF-8, LC_MESSAGES=en_AU.UTF-8, LC_PAPER=en_AU.UTF-8, LC_NAME=C, LC_ADDRESS=C, LC_TELEPHONE=C, LC_MEASUREMENT=en_AU.UTF-8 and LC_IDENTIFICATION=C

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: plotly(v.4.9.2), pander(v.0.6.3), glue(v.1.3.1), broom(v.0.5.4), ggrepel(v.0.8.1), matrixStats(v.0.55.0), scales(v.1.1.0), lubridate(v.1.7.4), magrittr(v.1.5), forcats(v.0.4.0), stringr(v.1.4.0), dplyr(v.0.8.4), purrr(v.0.3.3), readr(v.1.3.1), tidyr(v.1.0.2), tibble(v.2.1.3), ggplot2(v.3.2.1) and tidyverse(v.1.3.0)

loaded via a namespace (and not attached): Rcpp(v.1.0.3), lattice(v.0.20-40), assertthat(v.0.2.1), digest(v.0.6.25), mime(v.0.9), R6(v.2.4.1), cellranger(v.1.1.0), backports(v.1.1.5), reprex(v.0.3.0), evaluate(v.0.14), highr(v.0.8), httr(v.1.4.1), pillar(v.1.4.3), rlang(v.0.4.4), lazyeval(v.0.2.2), readxl(v.1.3.1), rstudioapi(v.0.11), data.table(v.1.12.8), rmarkdown(v.2.1), labeling(v.0.3), htmlwidgets(v.1.5.1), munsell(v.0.5.0), shiny(v.1.4.0), httpuv(v.1.5.2), compiler(v.3.6.3), modelr(v.0.1.6), xfun(v.0.12), pkgconfig(v.2.0.3), htmltools(v.0.4.0), tidyselect(v.1.0.0), fansi(v.0.4.1), viridisLite(v.0.3.0), later(v.1.0.0), crayon(v.1.3.4), dbplyr(v.1.4.2), withr(v.2.1.2), grid(v.3.6.3), xtable(v.1.8-4), nlme(v.3.1-144), jsonlite(v.1.6.1), gtable(v.0.3.0), lifecycle(v.0.1.0), DBI(v.1.1.0), cli(v.2.0.1), stringi(v.1.4.6), farver(v.2.0.3), promises(v.1.1.0), fs(v.1.3.1), xml2(v.1.2.2), generics(v.0.0.2), vctrs(v.0.2.3), tools(v.3.6.3), Cairo(v.1.5-10), hms(v.0.5.3), crosstalk(v.1.0.0), fastmap(v.1.0.1), yaml(v.2.2.1), colorspace(v.1.4-1), rvest(v.0.3.5), knitr(v.1.28) and haven(v.2.2.0)

Report prepared by the University of Adelaide, Bioinformatics Hub. https://www.adelaide.edu.au/bioinformatics-hub/